Ecological Orbits: How Planets Move and Populations Grow

Ecological Orbits: How Planets Move and Populations Grow

Volumn , Issue , 2007, Pages 1-184

  Ginzburg, Lev ^a   Colyvan, Mark ^b  

^a STONY BROOK UNIVERSITY   (United States)

^b UNIVERSITY OF QUEENSLAND   (Australia)

Author keywords

Differential equations; Inertial population growth; Laws of ecology; Maternal effect; Mathematical models; Philosophy of ecology; Philosophy of science; Population ecology

Indexed keywords

EID: 84940516674     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1093/acprof:oso/9780195168167.001.0001     Document Type: Book

References (169)

1. Abrams, P. A. 1994. The fallacies of ratio-dependent predation. Ecology 74: 1842-1850.
2. Abrams, P. A., and Ginzburg, L. R. 2000. The nature of predation: prey dependent, ratio dependent, or neither? Trends in Ecology and Evolution 15(8):337-341.
3. Abrams, P. A., Menge, B. A., Mittelbach, G. G., Spiller, D. A., and Yodzis, P. 1996. The role of indirect effects in food webs. In G. A. Polis and K. O. Winemiller (eds.), Food Webs:Integration of Patterns and Dynamics. New York: Chapman and Hall, p. 387.
4. Adler, F. R., and Morris, W. F. 1994. A general test for interaction modification. Nature. 75(6):1552-1559.
5. Akçakaya, H. R. 1992. Population cycles of mammals: evidence for a ratio-dependent predation hypothesis. Ecological Monographs 62: 119-142.
6. Akçakaya, H. R., Arditi, R., and Ginzburg, L. R. 1995. Ratio-dependent predation: an abstraction that works. Ecology 76(3):995-1004.
7. Akçakaya, H. R., Burgman, M. A., and Ginzburg, L. R. 1999. Applied Population Ecology:Principles and Computer Exercises. Sunderland, MA: Sinauer Associates.
8. Akçakaya, H. R., Ginzburg, L. R., Slice, D., and Slobodkin, L. B. 1988. The theory of population dynamics-II. Physiological delays. Bulletin of Mathematical Biology 50(5):503-515.
9. Anderson, R. M., and May, R. M. 1980. Infectious diseases and population cycles of forest insects. Science 210: 658-661.
10. Arditi, R. 1975. Etude de modeles theoriques de l'ecosysteme a deux especes proie predateur. Specialty Doctorate Thesis, University of Paris.
11. Arditi, R., and Ginzburg, L. R. 1989. Coupling in predator-prey dynamics: ratiodependence. Journal of Theoretical Biology 139: 311-326.
12. Arditi, R., Tyutyunov, Y., Morgulis, A., Govorukhin, V., and Senina, I. 2001. Directed movement of predators and the amergence of density-dependence in predator-prey models. Theoretical Population Biology 59: 207-221.
13. Armstrong, D. M. 1983. What Is a Law of Nature? Cambridge: Cambridge University Press.
14. Baltensweiler, W., and Fischlin, A. 1989. The larch budmoth in the Alps. In A. Berryman (ed.), Dynamics of Forest Insect Populations: Patterns, Causes and Implications. New York: Plenum Press, pp. 331-351.
15. Beckerman, A., Benton, T. G., Ranta, E., Kaitala, V., and Lundberg, P. 2002. Population dynamic consequences of delayed life-history effects. Trends in Ecology and Evolution 17: 263-269.
16. Beddington, J. R., Free, C. A., and Lawton, J. H. 1975. Dynamic complexity in predatorprey models framed in difference equations. Nature 225: 58-60.
17. Beddington, J. R., Free, C. A., and Lawton, J. H. 1976. Concepts of stability and resilience in predator-prey models. Journal of Animal Ecology 45: 791-816.
18. Bell, E. T. 1953. Men of Mathematics. London: Penguin.
19. Berezovskaya, F., Karev, G., and Arditi, R. 2001. Parametric analysis of the ratiodependent predator-prey model. Journal of Mathematical Biology 43: 221-246.
20. Berryman, A. A. 1995. Population cycles: a critique of the maternal and allometric hypotheses. Journal of Animal Ecology 64: 290-293.
21. Berryman, A. A. 1999. Principles of Population Dynamics and Their Application. Cheltenham, UK: Stanley Thornes Publishers.
22. Berryman, A. A. (ed.) 2002. Population Cycles: The Case for Trophic Interactions. New York: Oxford University Press.
23. Billick, I., and Case, T. J. 1994. Higher order interactions in ecological communities: what are they and how can they be detected? Nature 75(6):1529-1543.
24. Bjornstad, O. N., and Grenfell, B. 2001. Noisy clockwork: time series analysis of population fluctuations in animals. Science 293: 638-643.
25. Blackburn, T. M., and Gaston, K. J. 2001. Linking patterns in macroecology. Journal of Animal Ecology 70: 338-352.
26. Bonner, J. T. 1965. Size and Cycle. Princeton, NJ: Princeton University Press.
27. Boonstra, R. 1994. Population cycles in microtines: the senescene hypothesis. Evolutionary Ecology 8: 196-219.
28. Boonstra, R., and Boag, P. T. 1987. A test of the Chitty hypothesis: inheritance of lifehistory traits in meadow voles Microtus pennsylvanicus. Evolution 41: 929-947.
29. Boonstra, R., Krebs, C. J., and Stenseth, N. C. 1998. Population cycles in small mammals:the problem of explaining the low phase. Ecology 79(5):1479-1488.
30. Brown, J. H. 1995. Macroecology. Chicago: University of Chicago Press.
31. Brown, J. H., and West, G. (eds.) 2000. Scaling in Biology. New York: Oxford University Press.
32. Brown, J. H., West, G. B., and Enquist, B. J. 2000. Scaling in biology: patterns and processes, causes and consequences. In J. H. Brown and G. B. West (eds.), Scaling in Biology. Oxford: Oxford University Press, pp. 1-24.
33. Bulmer, M. 1975. Phase relations in the ten-year cycle. Journal of Animal Ecology 44:609-621.
34. Burgman, M. A., Ferson, S., and Akcakaya, H. R. 1993. Risk Assessment in Conservation Biology. London: Chapman and Hall.
35. Calder, W. A. 1983. An allometric approach to population cycles of mammals. Journal of Theoretical Biology 100: 275-282.
36. Calder, W. A., III. 1984. Size, Function, and Life History. Mineola, NY: Dover edition, 1996.
37. Carbone, C., and Gittleman, J. L. 2002. A common rule for the scaling of carnivore density. Science 295: 2273-2276.
38. Cartwright, N. 1983. How the Laws of Physics Lie. New York: Oxford University Press.
39. Cartwright, N. 1999. The Dappled World: A Study of the Boundaries of Science. Cambridge: Cambridge University Press.
40. Chalmers, A. F. 1999. What Is This Thing Called Science? 3d ed. Brisbane: University of Queensland Press.
41. Charnov, E. L. 1993. Life History Invariants: Some Explorations of Symmetry in Evolutionary Ecology. Oxford: Oxford University Press.
42. Charnov, E. L., Haskell, J., and Ernest, S. K. M. 2001. Density-dependent invariance, dimensionles life histories and the energy-equivalence rule. Evolutionary Ecology Research 3: 117-127.
43. Clark, G. P. 1971. The second derivative in population modelling. Ecology 52: 606-613.
44. Clutton-Brock, T. H., Albon, S., and Guinness, F. 1987. Interactions between population density and maternal characteristics affecting fecundity and juvenile survival in red deer. Journal of Animal Ecology 56: 857-871.
45. Colyvan, M. 2001a. The Indispensability of Mathematics. New York: Oxford University Press.
46. Colyvan, M. 2001b. The miracle of applied mathematics. Synthese 127(3):265-278.
47. Colyvan, M. 2002. Mathematics and aesthetic considerations in science. Mind 111(441):69-74.
48. Colyvan, M., and Ginzburg, L. R. 2003a. The Galilean turn in population ecology. Biology and Philosophy, 18(3):401-414.
49. Colyvan, M., and Ginzburg, L. R. 2003b. Laws of nature and laws of ecology. Oikos 101(3):649-653.
50. Cooper, G. 1998. Generalizations in ecology: a philosophical taxonomy. Biology and Philosophy 13: 555-586.
51. Cosner, C., DeAngelis, D. L., Ault, J. S., and Olson, D. B. 1999. Effects of spatial grouping on the functional response of predators. Theoretical Population Biology 56: 65-75.
52. Damuth, J. 1981. Population density and body size in mammals. Nature 290: 699-700.
53. Damuth, J. 1987. Interspecific allometry of population density in mammals and other animals: the independence of body mass and population energy-use. Biological Journal of the Linnean Society 31: 193-246.
54. Damuth, J. 1991. Ecology: of size and abundance. Nature 351: 268-269.
55. Duhem, P. 1906. The Aim and Structure of Physical Theory. Princeton, NJ: Princeton University Press, 1954.
56. Dunbar, M. J. 1971. The evolutionary stability in marine environments: natural selection at the level of the ecosystem. In G. C. Williams (ed.), Group Selection. Chicago: Aldine Atherton, 125-135.
57. Dyson, F. J. 1964. Mathematics in the physical sciences. Scientific American 211(3):128-146.
58. Easterlin, R. 1961. The American baby-boom in historical perspective. American Economic Review 51: 860-911.
59. Elton, C. 1927. Animal Ecology. Chicago: University of Chicago Press, 2001.
60. Elton, C., and Nicholson, M. 1942. The ten year cycle in numbers of lynx in Canada. Animal Ecology 2: 215-244.
61. Enquist, B. J., Brown, J. H., and West, G. B. 1998. Allometric scaling of plant energetics and population density. Nature 395: 163-165.
62. Fenchel, T. 1974. Intrinsic rate of natural increase: the relationship with body size. Oecologia 14: 317-326.
63. Ferson, S., and Burgman, M. A. (eds.) 2000. Quantitative Methods for Conservation Biology. New York: Springer-Verlag.
64. Feynman, R. 1965. The Character of Physical Law. London: British Broadcasting Corporation.
65. Feynman, R., Leighton, R., and Sands, M. 1963. The Feynman Lectures on Physics. Reading, MA: Addison-Wesley.
66. Frauenthal, J. 1975. A dynamic model for human population growth. Theoretical Population Biology 8: 64-73.
67. Ginzburg, L. R. 1972. The analogies of the "free motion" and "force" concepts in population theory (in Russian). In V. A. Ratner (ed.), Studies on Theoretical Genetics. Novosibirsk, USSR: Academy of Sciences of the USSR, pp. 65-85.
68. Ginzburg, L. R. 1986. The theory of population dynamics: I. Back to first principles. Journal of Theoretical Biology 122: 385-399.
69. Ginzburg, L. R. 1992. Evolutionary consequences of basic growth equations. Trends in Ecology and Evolution 7: 133; correspondence, 314-317; further letters, 1993, 8: 68-71.
70. Ginzburg, L. R. 1998. Inertial growth: population dynamics based on maternal effects. In T. A. Mousseau and C. W. Fox (eds.), Maternal Effects as Adaptions. New York: Oxford University Press, pp. 42-53.
71. Ginzburg, L. R., and Akçakaya, H. R. 1992. Consequences of ratio-dependent predation for steady state properties of ecosystems. Ecology 73(5):1536-1543.
72. Ginzburg, L. R., Akcakaya, H. R., Slice, D., and Slobodkin, L. B. 1988. Balanced growth rates vs. balanced accelerations as causes of ecological equilibria. In L. M. Ricciardi (ed.), Biomathematics and Related Computational Problems. The Netherlands: Kluwer Academic Publishers, pp. 165-175.
73. Ginzburg, L. R., Goldman, Y. I., and Rahkin, A. I. 1971. A mathematical model of interaction between two populations I. Predator prey (in Russian). Zhurnal Obshchei Biologii 32:724-730.
74. Ginzburg, L. R., and Inchausti, P. 1997. Asymmetry of population cycles: abundancegrowth representation of hidden causes of ecological dynamics. Oikos 80: 435-447.
75. Ginzburg, L. R., and Jensen, C. X. J. (forthcoming). Rules of thumb for judging ecological theories. Trends in Ecology and Evolution.
76. Ginzburg, L. R., Konovalov, N. Y., and Epelman, G. S. 1974. A mathematical model of interaction between two populations. IV. Comparison of theory and experimental data (in Russian). Zhurnal Obshchei Biolgii 35: 613-619.
77. Ginzburg, L. R., and Taneyhill, D. E. 1994. Population cycles of forest Lepidoptera: a maternal effect hypothesis. Journal of Animal Ecology 63: 79-92.
78. Ginzburg, L. R., and Taneyhill, D. 1995. Higher growth rate implies shorter cycle, whatever the cause: a reply to Berryman. Journal of Animal Ecology 64: 294-295.
79. Hanski, I., Henttonen, H., Korpimaki, E., Oksanen, L., and Turchin, P. 2001. Small-rodent dynamics and predation. Ecology 82(6):1505-1520.
80. Harvey, P. H., and Pagel, M. D. 1991. The Comparative Method of Evolutionary Biology. New York: Oxford University Press.
81. Hemmingsen, A. M. 1960. Energy metabolism as related to body size and respiratory surfaces, and its evolution. Reports of the Steno Memorial Hospital and the Nordisk Insulin Labatorium. Volume IX, Part II. Princeton, NJ: Novo Nordisk, pp. 6-110.
82. Hempel, C. G. 1965. Aspects of Scientific Explanation and Other Essays in the Philosophy of Science. London: Macmillan.
83. Henttonen, H., Oksanen, L., Jortikka, T., and Hauksalami, V. 1987. How much do weasels shape microtine cycles in the northern Fennoscandian taiga? Oikos 50: 353-365.
84. Holland, M. M., Lawrence, D. M., and Morrin, D. J. (eds.) 1992. Profiles of Ecologists:Results of a Survey of the Membership of the Ecological Society of America. Washington, DC: Ecological Society of America.
85. Hörnfeldt, B. 1994. Delayed density dependence as a determinant of vole cycles. Ecology 75: 791-806.
86. Hsu, S.-B., Hwang, T.-W., and Kuamg, Y. 2001. Global analysis of the Michaelis-Mententype ratio-dependent predator-prey system. Journal of Mathematical Biology 42: 489-506.
87. Inchausti, P., and Ginzburg, L. R. 1998. Small mammal cycles in northern Europe: pattern and evidence for a maternal effect hypothesis. Journal of Animal Ecology 67: 180-194.
88. Inchausti, P., and Ginzburg, L. R. 2002. Using the phase shift for assessing the causation of population cycles. Ecological Modeling 152: 89-102.
89. Inchausti, P., and Halley, J. 2001. Investigating long-term ecological variability using the global population dynamics database. Science 293: 655-657.
90. Jost, C., Arino, O., and Arditi, R. 1999. About deterministic extinction in ratio-dependent predator-prey models. Bulletin of Mathematical Biology 61: 19-32.
91. Jost, C., and Ellner, S. P. 2000. Testing for predator dependence in predator-prey dynamics: a non-parametric approach. Proceedings of the Royal Society of London. Series B. Biological Sciences 267(1453):1611-1620.
92. Kareiva, P. M. 1994. Higher order interactions as a foil to reductionist ecology. Nature 75(6):1527-1528.
93. King, A. A., and Shaffer, W. 2001. The geometry of a population cycle: a mechanistic model of snowshoe hare demography. Ecology 82(3):814-830.
94. Kingsland, S. E. 1985. Modelling Nature: Episodes in the History of Population Ecology. Chicago: University of Chicago Press.
95. Kitcher, P. 1981. Explanatory unification. Philosophy of Science 48: 507-531.
96. Kleiber, M. 1975. The Fire of Life, 2d ed. New York: Krieger.
97. Krebs, C. J., Boonstra, R., Boutin, S., and Sinclair, A. R. E. 2001a. What drives the 10-year cycle of snowshoe hares? Bioscience 51(1):25-35.
98. Krebs, C. J., Boutin, S., and Boonstra, R. (eds.) 2001b. Ecosystem Dynamics of the Boreal Forest: The Kluane Project. New York: Oxford University Press.
99. Krebs, C. J., Boutin, S., Boonstra, R., Sinclair, A. R. E., Smith, J. N. M., Dale, M. R. T., Martin, K., and Turkington, R. 1995. Impact of food and predation on the snowshoe hare cycle. Science 269: 1112-1115.
100. Krukonis, G., and Schaffer, W. M. 1991. Population cycles in mammals and birds: does periodicity scale with body size? Journal of Theoretical Biology 148: 469-493.
101. Lakatos, I. 1970. Falsification and the methodology of scientific research programmes. In I. Lakatos and A. Musgrave (eds.), Criticism and the Growth of Knowledge. Cambridge:Cambridge University Press, pp. 91-195.
102. Lauwerier, H. A. 1986. Two-dimensional iterative maps. In A. V. Holden (ed.), Chaos. Princeton, NJ: Princeton University Press, chap. 4.
103. Lauwerier, H. A., and Metz, J. A. J. 1986. Hopf bifurcation in host-parasitoid models. Journal of Mathematics in Applied Medicine and Biology 3: 191-210.
104. Lawton, J. H. 1989. What is the relationship between population density and body size in animals? Oikos 55: 429-434.
105. Lawton, J. H. 1999. Are there general laws in biology? Oikos 84: 177-192.
106. Luckinbill, L. S. 1973. Coexistence in laboratory populations of paramecium aurelia and its predator didinium nasutum. Ecology 54(6):1320-1327.
107. MacArthur, R. 1972. Coexistence of species. In J. A. Behnke (ed.), Challenging Biological Problems: Directions towards Their Solution. New York: Oxford University Press, pp. 253-259.
108. May, R. M. 1974a. Stability and Complexity in Model Ecosystems, 2d ed. Princeton, NJ:Princeton University Press.
109. May, R. M. 1974b. Biological populations with nonoverlapping generations: stable cycles and chaos. Science 186: 645-647.
110. McCarthy, M. A., Ginzburg, L. R., and Akakaya, H. R. 1995. Predator interference across trophic chains. Ecology 76(4):1310-1319.
111. McCauley, E., and Murdoch, W. 1985. Cyclic and stable populations: plankton as a paradigm. American Naturalist 129: 97-121.
112. Middleton, A. 1934. Periodic fluctuations in British game populations. Journal of Animal Ecology 3: 231-249.
113. Millar, J. S., and Zammuto, R. M. 1983. Life histories of mammals: an analysis of life tables. Ecology 64(4):631-635.
114. Morin, P. J. 1999. Community Ecology. Malden: Blackwell Science.
115. Mousseau, T. A., and Fox, C. W. (eds.) 1998. Maternal Effects as Adaptions. New York:Oxford University Press.
116. Murdoch, W. W. 1970. Population regulation and population inertia. Ecology 51(3):497-502.
117. Murdoch, W. W., Briggs, C., and Nisbet, R. 2003. Consumer-Resource Dynamics. Princeton, NJ: Princeton University Press.
118. Murdoch, W. W., Kendall, B. E., Nisbet, R. M., Briggs, C. J., McCauley, E., and Bolser, R. 2002. Single-species models for many-species food webs. Nature 417: 541-543.
119. Murray, B. M., Jr. 1992. Research methods in physics and biology. Oikos 64(3):594-596.
120. Murray, B. M., Jr. 1999. Is theoretical ecology a science? Oikos 87: 594-600.
121. Myers, J. H. 1988. Can a general hypothesis explain population cycles of forest Lepidoptera? Advances in Ecological Research 18: 179-242.
122. National Environment Research Council (NERC). 1999. The Global Copulation Dynamics Database. NERC Centre for Population Biology, Imperial College. Available:. Accessed 6/13/2002.
123. Nee, S., Read, A. F., Greenwood, J. J. D., and Harvey, P. H. 1991. The relationship between abundance and body size in British birds. Nature 351: 312-313.
124. Neutel, A., Heesterbeek, J., and de Ruiter, P. 2002. Stability in real food webs: weak links in long loops. Science 296: 1120-1123.
125. Newton-Smith, W. H. 2000. A Companion to the Philosophy of Science. Oxford: Blackwell.
126. Pastorok, R. A., Bartell, S. M., Ferson, S., and Ginzburg, L. R. (eds.) 2002. Ecological Modeling in Risk Assessment. Boca Raton: CRC Press.
127. Peek, J., Urich, D., and Mackie, R. 1976. Moose habitat selection and relationship to forest management in northeastern Minnesota. Wildlife Monographs 48: 6-65.
128. Peterson, R. O., Page, R. E., and Dodge, K. M. 1984. Wolves, moose, and the allometry of population cycles. Science 224(4655):1350-1352.
129. Peterson, R. O., and Vucetich, J. A. 2002. Ecological studies of Wolves on Isle Royal, Annual Report 2001-2002. Houghton, MI: School of Forestry and Wood Products, Michigan Technological University.
130. Plato (P. Shorey, trans.) 1930. The Republic. Cambridge, MA: Harvard University Press.
131. Purcell, E. M. 1977. Life at low Reynolds number. American Journal of Physics 45(1):3-11.
132. Quenette, P. Y., and Gerard, J. F. 1993. Why biologists do not think like physicists. Oikos 68(2):361-363.
133. Quine, W. V. 1951. Five milestones of empiricism. In Theories and Things. Cambridge, MA: Harvard University Press, 1981, pp. 67-72.
134. Quine, W. V. 1960. Word and Object. New York: MIT Press and John Wiley and Sons.
135. Quine, W. V. 1980. Two dogmas of empiricism. In From a Logical Point of View, 2d ed. Cambridge, MA: Harvard University Press, pp. 20-46.
136. Quine, W. V. 1995. From Stimulus to Science. Cambridge, MA: Harvard University Press.
137. Quine, W. V., and Ullian, J. S. 1978. The Web of Belief, 2d ed. New York: McGraw-Hill.
138. Reiss, M. H. 1989. The Allometry of Growth and Reproduction. Cambridge: Cambridge University Press.
139. Rossiter, M. C. 1991. Environmentally based maternal effects: a hidden force in population dynamics. Oecologia 87: 288-294.
140. Rossiter, M. 1998. The role of environmental variation in parental effects expression. In T. A. Mousseau and C. W. Fox (eds.), Maternal Effects as Adaptations. New York: Oxford University Press, pp. 113-134.
141. Royama, T. 1992. Analytical Population Dynamics. London: Chapman and Hall.
142. Schaffer, W. M., Pederson, B. S., Moore, B. K., Skarpaas, O., King, A. A., and Bronnikova, T. V. 2001. Sub-harmonic resonance and multi-annual oscillations in northern mammals: a non-linear dynamical systems perspective. Chaos Solutions and Fractals 12(2):251-264.
143. Seldal, T., Amndersen, K., and Hodgstedt, G. 1994. Grazing-induced proteins inhibitors: a possible cause for lemming population cycles. Oikos 70: 3-11.
144. Skalski, G. T., and Gilliam, J. F. 2001. Functional responses with predator interference:viable alternatives to the Holling type II model. Ecology 82(11):3083-3092.
145. Slobodkin, L. 2003. A Citizen's Guide to Ecology. New York: Oxford University Press.
146. Slobodkin, L. B. 1961. Growth and Rejuvenation of Animal Populations, 2d ed. New York:Dover, 1980.
147. Smart, J. J. C. 1968. Between Philosophy and Science: An Introduction to the Philosophy of Science. New York: Random House.
148. Sobel, D. 1999. Galileo's Daughter: A Historical Memoir of Science, Faith, and Love. New York: Walker and Company.
149. Southwood, T. R. E. 1976. Bionomic strategies and population parameters. In R. M. May (ed.), Theoretical Ecology: Principles and Applications. Philadelphia: Saunders, pp. 26-48.
150. Spencer, D., and Lensink, C. 1970. The muskox of the Nunivak Island, Alaska. Journal of Wildlife Management 34: 1-15.
151. Steiner, M. 1998. The Applicability of Mathematics as a Philosophical Problem. Cambridge, MA: Harvard University Press.
152. Stenseth, N. C. 1999. Population cycles in voles and lemmings: density dependence and phase dependence in a stochastic world. Oikos 87(2): 427-461
153. Taneyhill, D. 1993. The logistic equation: final installment. Trends in Ecology and Evolution 8: 68-70.
154. Turchin, P. 2001. Does population ecology have general laws? Oikos 94(1):17-26.
155. Turchin, P. 2003a. Complex Population Dynamics: A Theoretical/Empirical Synthesis. Princeton, NJ: Princeton University Press.
156. Turchin, P. 2003b. Historical Dynamics: Why States Rise and Fall. Princeton, NJ:Princeton University Press.
157. Turchin, P., and Batzli, G. 2001. Availability of food and the population dynamics of arvicoline rodents. Ecology 82: 1521-1534.
158. Turchin, P., and Hanski, I. 2001. Contrasting alternative hypotheses about rodent cycles be translating them into parameterized models. Ecology Letters 4: 267-276.
159. Vadasz, A. S., Vadasz, P., Abashar, M. E., and Gupthar, A. S. 2001. Recovery of an oscillatory mode of batch yeast growth in water for a pure culture. International Journal of Food Microbiology 71(2-3): 219-234.
160. Vadasz, A. S., Vadasz, P., Abashar, M. E., and Gupthar, A. S. 2002. Theoretical and experimental recovery of oscillations during batch growth of a mixed culture of yeast in water. World Journal of Microbiology and Biotechnology 18(3):239-246.
161. van Fraassen, B. C. 1980. The Scientific Image. Oxford: Clarendon.
162. van Fraassen, B. C. 1989. Laws and Symmetry. Oxford: Clarendon.
163. Veilleux, B. G. 1979. An analysis of the predatory interaction between paramecium and didinium. Journal of Animal Ecology 48(3):787-803.
164. Vucetich, J. A., Peterson, R. O., and Schaefer, C. L. 2002. The effect of prey and predator densities on wolf predation. Ecology 83: 3003-3013.
165. Wellington, W. G. 1957. Individual differences as a factor in population dynamics: the development of a problem. Canadian Journal of Zoology 35: 293-323.
166. West, G. B., Brown, J. H., and Enquist, B. J. 1999. The fourth dimension of life: fractal geometry and allometric scaling of organisms. Science 284: 1677-1679.
167. Wigner, E. P. 1960. The unreasonable effectiveness of mathematics in the natural sciences. Communications on Pure and Applied Mathematics 13: 1-14.
168. Wooton, J. T. 1994. Putting the pieces together: testing the independence of interactions among organisms. Nature 75(6):1544-1551.
169. Xiao, D., and Ruan, S. 2001. Global dynamics of a ratio-dependent predator-prey system. Journal of Mathematical Biology 43(3):268-290.